```Date: Feb 2, 2013 3:36 AM
Author: William Elliot
Subject: Re: closed but not complete

On Fri, 1 Feb 2013, Butch Malahide wrote:> On Feb 1, 9:14 pm, William Elliot <ma...@panix.com> wrote:> > On Fri, 1 Feb 2013, Daniel J. Greenhoe wrote:> >> > > Let (Y,d) be a subspace of a metric space (X,d).> >> > > If (Y,d) is complete, then Y is closed with respect to d. That is, > > > complete==>closed.> >> > > Alternatively, if (Y,d) is complete, then Y contains all its limit > > > points.> > > Would anyone happen to know of a counterexample for the converse? > > > That is, does someone know of any example that demonstrates that > > > closed --> complete is *not* true?> >> > No. Assume K is a closed subset of the complete space (S,d).> > But the original poster did not say that his metric space (X,d) was> complete.> Oh, so any closed subset of Q is an example.Given that A subset Q, is open or closed, what's the probablity that it's clopen?Whops, here's the simple version.  A subset of a linear order is consider to be an interval when it's order convex.Given an open or a closed interval of Q, what's the probablity that it's clopen?
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